Correspondence theorem (group theory)

In the area of mathematics known as group theory, the correspondence theorem, sometimes referred to as the fourth isomorphism theorem or the lattice theorem, states that if is a normal subgroup of a group , then there exists a bijection from the set of all subgroups of containing , onto the set of all subgroups of the quotient group . The structure of the subgroups of is exactly the same as the structure of the subgroups of containing , with collapsed to the identity element.